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Formulas: Probability
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Q1: In a bag, there are 7 red marbles, 5 blue marbles, and 4 green marbles. Two marbles are randomly selected from the bag without replacement. What is the probability that both of them are blue?
Sol:
For the first draw, Probability of selecting a blue marble is 5/16 (5 blue marbles out of 16 total marbles).
After the first marble is drawn, there are 4 blue marbles left out of 15 total marbles.
For the second draw, the probability of selecting a blue marble is 4/15.
To calculate the probability of both marbles being blue =>
Probability = 20/24 = 1/22
Q2: In a bag, there are 3 green bulbs, 4 orange bulbs, and 5 white bulbs. A bulb is randomly picked from the bag. What is the probability of selecting either a green bulb or a white bulb?
Sol:
Total number of bulbs in the bag is 3 green + 4 orange + 5 white = 12 bulbs
Number of green bulbs is 3, and the number of white bulbs is 5
Probability of selecting either a green or a white bulb, we add the number of green bulbs and the number of white bulbs, and then divide it by the total number of bulbs.
Probability = (Number of green bulbs + Number of white bulbs) / Total number of bulbs
Probability = 8/12
Probability = 2/3
Q3: Joey Tribbiani organized a rack race with two participants. The probability of the first participant winning is 2/7, and the probability of the second participant winning is 3/5. What is the probability that one of them will win?
Sol:
Let’s denote:
P(A) = Probability of the first participant winning = 2/7
P(B) = Probability of the second participant winning = 3/5
The probability of both participants winning simultaneously (a tie) is zero since there can only be one winner. Therefore, the probability that one of them will win is:
P(one of them wins) = P(A) + P(B) – P(A and B)
P(one of them wins) = P(A) + P(B) – 0 (since P(A and B) = 0)
P(one of them wins) = P(A) + P(B)
Substituting the given probabilities:
Q4: In a drawer, there are 4 black pens, 3 blue pens, and 5 red pens. A pen is drawn at random from the drawer. What is the probability that it is either black or blue?
Sol:
We have calculate the probability of drawing a black or blue pen from the drawer
The total no. of pens in the drawer is 4 black + 3 blue + 5 red = 12 pens
Probability of drawing a black pen is 4/12
Probability of drawing a blue pen is 3/12 = 1/4
Hence, The probability of drawing either a black or blue pen, we add the individual probabilities:
Probability = 4/12 + 3/12
Probability = 7/12
Q5: Sylvester Stallone brought a box of balloons for a group of students. The box contains 3 balloons of Shape A, 4 balloons of Shape B, and 5 balloons of Shape C. If three balloons are randomly drawn from the box, what is the probability that all three balloons are of different shapes?
Sol:
Total No. of Balloons = 3 Balloons of Shape A +4 Balloons of Shape B + 5 Balloons of Shape C = 12
n(s)= 12C3 = 220
n(e)= 3C1 ∗ 4C1 ∗ 5C1 = 60
P= 60/220 = 3/11
314 videos|170 docs|185 tests
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1. What is the definition of probability? |
2. How is probability calculated? |
3. Can the probability of an event be greater than 1? |
4. What is the meaning of mutually exclusive events in probability? |
5. How do you calculate the probability of independent events? |
314 videos|170 docs|185 tests
|