Page 1
1. List the outcomes you can see in these experiments
Solution:
(i) The outcomes in spinning wheel = A, A, A, B, C, D
(ii) The outcomes in drawing a ball from a bag containing 5 identical balls
of different colours = White, Red, Blue, Green, Yellow
2. A die is rolled once. Find the probability of getting
(i) an even number
(ii) a multiple of 3
(iii) not a multiple of 3
Solution:
Total outcomes of a die when rolled once:
1, 2, 3, 4, 5, 6 = 6
Page 2
1. List the outcomes you can see in these experiments
Solution:
(i) The outcomes in spinning wheel = A, A, A, B, C, D
(ii) The outcomes in drawing a ball from a bag containing 5 identical balls
of different colours = White, Red, Blue, Green, Yellow
2. A die is rolled once. Find the probability of getting
(i) an even number
(ii) a multiple of 3
(iii) not a multiple of 3
Solution:
Total outcomes of a die when rolled once:
1, 2, 3, 4, 5, 6 = 6
(i) An even number: 2, 4, 6
i.e., Favourable outcomes = 3
Therefore,
Probability P(E) =
=
(ii) Multiple of 3 = 3, 6
i.e., Favourable outcomes = 2
Therefore,
Probability P(E) =
=
(iii) Not a multiple of 3 = 1, 2, 4, 5
i.e. Favourable outcomes = 4
Therefore,
Probability P(E) =
=
3. Two coins are tossed together. Find the probability of getting
(i) Two tails
(ii) At least one tail
(iii) No tail
Solution:
The total outcomes, when two coins are tossed together = 2 × 2 = 4
Therefore, outcomes are,
HH, HT, TH, TT
(i) Favourable outcomes of getting two tails = 1
Page 3
1. List the outcomes you can see in these experiments
Solution:
(i) The outcomes in spinning wheel = A, A, A, B, C, D
(ii) The outcomes in drawing a ball from a bag containing 5 identical balls
of different colours = White, Red, Blue, Green, Yellow
2. A die is rolled once. Find the probability of getting
(i) an even number
(ii) a multiple of 3
(iii) not a multiple of 3
Solution:
Total outcomes of a die when rolled once:
1, 2, 3, 4, 5, 6 = 6
(i) An even number: 2, 4, 6
i.e., Favourable outcomes = 3
Therefore,
Probability P(E) =
=
(ii) Multiple of 3 = 3, 6
i.e., Favourable outcomes = 2
Therefore,
Probability P(E) =
=
(iii) Not a multiple of 3 = 1, 2, 4, 5
i.e. Favourable outcomes = 4
Therefore,
Probability P(E) =
=
3. Two coins are tossed together. Find the probability of getting
(i) Two tails
(ii) At least one tail
(iii) No tail
Solution:
The total outcomes, when two coins are tossed together = 2 × 2 = 4
Therefore, outcomes are,
HH, HT, TH, TT
(i) Favourable outcomes of getting two tails = 1
Hence,
Probability P(E) =
(ii) Favourable outcomes of getting at least one tail = TH, HT, TT = 3
Hence,
Probability P(E) =
(iii) Favourable outcomes of getting no tail = HH = 1
Hence,
Probability P(E) =
4. Three coins are tossed together. Find the probability of getting
(i) At least two heads
(ii) At least one tail
(iii) At most one tail
Solution:
Three coins are tossed together
Hence,
Total outcomes = 8
= HHH, HHT, HTH, THH, HTT, TTH, TTT, THT
(i) Favourable outcomes of getting at least two heads = HHH, HHT, HTH,
THH
= 4 in numbers
Therefore,
Page 4
1. List the outcomes you can see in these experiments
Solution:
(i) The outcomes in spinning wheel = A, A, A, B, C, D
(ii) The outcomes in drawing a ball from a bag containing 5 identical balls
of different colours = White, Red, Blue, Green, Yellow
2. A die is rolled once. Find the probability of getting
(i) an even number
(ii) a multiple of 3
(iii) not a multiple of 3
Solution:
Total outcomes of a die when rolled once:
1, 2, 3, 4, 5, 6 = 6
(i) An even number: 2, 4, 6
i.e., Favourable outcomes = 3
Therefore,
Probability P(E) =
=
(ii) Multiple of 3 = 3, 6
i.e., Favourable outcomes = 2
Therefore,
Probability P(E) =
=
(iii) Not a multiple of 3 = 1, 2, 4, 5
i.e. Favourable outcomes = 4
Therefore,
Probability P(E) =
=
3. Two coins are tossed together. Find the probability of getting
(i) Two tails
(ii) At least one tail
(iii) No tail
Solution:
The total outcomes, when two coins are tossed together = 2 × 2 = 4
Therefore, outcomes are,
HH, HT, TH, TT
(i) Favourable outcomes of getting two tails = 1
Hence,
Probability P(E) =
(ii) Favourable outcomes of getting at least one tail = TH, HT, TT = 3
Hence,
Probability P(E) =
(iii) Favourable outcomes of getting no tail = HH = 1
Hence,
Probability P(E) =
4. Three coins are tossed together. Find the probability of getting
(i) At least two heads
(ii) At least one tail
(iii) At most one tail
Solution:
Three coins are tossed together
Hence,
Total outcomes = 8
= HHH, HHT, HTH, THH, HTT, TTH, TTT, THT
(i) Favourable outcomes of getting at least two heads = HHH, HHT, HTH,
THH
= 4 in numbers
Therefore,
Probability P(E) =
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=
=
(ii) Favourable outcomes of getting at least one tail = HHT, HTH, HTT,
TTT, THH, THT, TTH
= 7 in numbers
Therefore,
Probability P(E)
= (Number of favourable outcome) / (Number of possible outcome)
=
(iii) Favorable outcomes of getting at most one tail = HHH, HHT, HTH,
THH
= 4 in numbers
Therefore,
Probability P(E) =
!"!# $%
&''(# $%
=
=
5. Two dice are rolled simultaneously. Find the probability of getting
(i) The sum as 7
(ii) The sum as 3 or 4
Page 5
1. List the outcomes you can see in these experiments
Solution:
(i) The outcomes in spinning wheel = A, A, A, B, C, D
(ii) The outcomes in drawing a ball from a bag containing 5 identical balls
of different colours = White, Red, Blue, Green, Yellow
2. A die is rolled once. Find the probability of getting
(i) an even number
(ii) a multiple of 3
(iii) not a multiple of 3
Solution:
Total outcomes of a die when rolled once:
1, 2, 3, 4, 5, 6 = 6
(i) An even number: 2, 4, 6
i.e., Favourable outcomes = 3
Therefore,
Probability P(E) =
=
(ii) Multiple of 3 = 3, 6
i.e., Favourable outcomes = 2
Therefore,
Probability P(E) =
=
(iii) Not a multiple of 3 = 1, 2, 4, 5
i.e. Favourable outcomes = 4
Therefore,
Probability P(E) =
=
3. Two coins are tossed together. Find the probability of getting
(i) Two tails
(ii) At least one tail
(iii) No tail
Solution:
The total outcomes, when two coins are tossed together = 2 × 2 = 4
Therefore, outcomes are,
HH, HT, TH, TT
(i) Favourable outcomes of getting two tails = 1
Hence,
Probability P(E) =
(ii) Favourable outcomes of getting at least one tail = TH, HT, TT = 3
Hence,
Probability P(E) =
(iii) Favourable outcomes of getting no tail = HH = 1
Hence,
Probability P(E) =
4. Three coins are tossed together. Find the probability of getting
(i) At least two heads
(ii) At least one tail
(iii) At most one tail
Solution:
Three coins are tossed together
Hence,
Total outcomes = 8
= HHH, HHT, HTH, THH, HTT, TTH, TTT, THT
(i) Favourable outcomes of getting at least two heads = HHH, HHT, HTH,
THH
= 4 in numbers
Therefore,
Probability P(E) =
!"!# $%
&''(# $%
=
=
(ii) Favourable outcomes of getting at least one tail = HHT, HTH, HTT,
TTT, THH, THT, TTH
= 7 in numbers
Therefore,
Probability P(E)
= (Number of favourable outcome) / (Number of possible outcome)
=
(iii) Favorable outcomes of getting at most one tail = HHH, HHT, HTH,
THH
= 4 in numbers
Therefore,
Probability P(E) =
!"!# $%
&''(# $%
=
=
5. Two dice are rolled simultaneously. Find the probability of getting
(i) The sum as 7
(ii) The sum as 3 or 4
(iii) Prime numbers on both the dice.
Solution:
Two dice are rolled simultaneously, then
Total outcomes = 6 × 6 = 36
(i) Sum as 7 = (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) = 6
Therefore,
Probability P(E) =
)!"!# $%
*$!# $%
=
=
(ii) The sum as 3 or 4 = (1, 2), (1, 3), (2, 1), (2, 2), (3, 1) = 5
Therefore,
Probability P(E) =
)!"!# $%
*$!# $%
=
(iii) Prime numbers on both the side
= (2, 2), (2, 3), (2, 5), (3, 2), (3, 3), (3, 5), (5, 2), (5, 3), (5, 5)
= 9
Therefore,
Probability P(E) =
)!"!# $%
*$!# $%
=
=
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