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)= ^{12}C_{3 }= 220
n(e)= ^{3}C_{1 }∗ ^{4}C_{1 }∗ ^{5}C_{1 }= 60
P= 60/220 = 3/11
314 videos170 docs185 tests

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 videos170 docs185 tests


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