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When unbiased coins are tossed. The probability of obtaining not more than 3 heads is
- a)¾
- b)½
- c)1
- d)0
Correct answer is option 'C'. Can you explain this answer?
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When unbiased coins are tossed. The probability of obtaining not more ...
Solution:
Given, unbiased coins are tossed.
We need to find the probability of obtaining not more than 3 heads.
Let us consider the possible outcomes when 4 coins are tossed:
- All tails: TTTT
- One head: HTTT, THTT, TTHT, TTTH
- Two heads: HHTT, HTHT, HTTH, THHT, THTH, TTHH
- Three heads: HHHT, HHTH, HTHH, THHH
- All heads: HHHH
Out of these possible outcomes, there are 4 outcomes where we obtain not more than 3 heads.
Therefore, the probability of obtaining not more than 3 heads = 4/16 = 1/4 = 0.25.
Hence, the correct answer is option 'C'.
Note: The probability of obtaining not more than 3 heads can also be calculated using the binomial distribution formula as follows:
P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
where X is the number of heads obtained in 4 tosses of a coin.
Using the binomial distribution formula, we get:
P(X ≤ 3) = (4C0 * (1/2)^0 * (1/2)^4) + (4C1 * (1/2)^1 * (1/2)^3) + (4C2 * (1/2)^2 * (1/2)^2) + (4C3 * (1/2)^3 * (1/2)^1)
= (1 * 1 * 1/16) + (4 * 1/2 * 1/8) + (6 * 1/4 * 1/4) + (4 * 1/8 * 1/2)
= 1/16 + 1/4 + 3/16 + 1/8
= 1/4
Therefore, the probability of obtaining not more than 3 heads = 1/4 = 0.25.
Given, unbiased coins are tossed.
We need to find the probability of obtaining not more than 3 heads.
Let us consider the possible outcomes when 4 coins are tossed:
- All tails: TTTT
- One head: HTTT, THTT, TTHT, TTTH
- Two heads: HHTT, HTHT, HTTH, THHT, THTH, TTHH
- Three heads: HHHT, HHTH, HTHH, THHH
- All heads: HHHH
Out of these possible outcomes, there are 4 outcomes where we obtain not more than 3 heads.
Therefore, the probability of obtaining not more than 3 heads = 4/16 = 1/4 = 0.25.
Hence, the correct answer is option 'C'.
Note: The probability of obtaining not more than 3 heads can also be calculated using the binomial distribution formula as follows:
P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
where X is the number of heads obtained in 4 tosses of a coin.
Using the binomial distribution formula, we get:
P(X ≤ 3) = (4C0 * (1/2)^0 * (1/2)^4) + (4C1 * (1/2)^1 * (1/2)^3) + (4C2 * (1/2)^2 * (1/2)^2) + (4C3 * (1/2)^3 * (1/2)^1)
= (1 * 1 * 1/16) + (4 * 1/2 * 1/8) + (6 * 1/4 * 1/4) + (4 * 1/8 * 1/2)
= 1/16 + 1/4 + 3/16 + 1/8
= 1/4
Therefore, the probability of obtaining not more than 3 heads = 1/4 = 0.25.
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Community Answer
When unbiased coins are tossed. The probability of obtaining not more ...
If the question is 3 unbiased coin is toss then possibility of getting 3 head is only 1 time so the answer is 1
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