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A die is rolled twice. What is the probability of getting a sum equal to 9?
Total number of outcomes possible when a die is rolled = 6 (∵ any one face out of the 6 faces)
E = Getting a sum of 9 when the two dice fall = {(3,6), (4,5), (5,4), (6,3)}
When tossing two coins once, what is the probability of heads on both the coins?
Total number of outcomes possible when a coin is tossed = 2 (∵ Head or Tail)
E = event of getting heads on both the coins = {HH}
What is the probability of getting a number less than 4 when a die is rolled?
One card is randomly drawn from a pack of 52 cards. What is the probability that the card drawn is a face card(Jack, Queen or King)
A dice is thrown. What is the probability that the number shown in the dice is divisible by 3?
John draws a card from a pack of cards. What is the probability that the card drawn is a card of black suit?
Total number of cards, n(S) = 52
Total number of black cards, n(E) = 26
Three coins are tossed. What is the probability of getting at most two tails?
Total number of outcomes possible when a coin is tossed = 2 (∵ Head or Tail)
E = event of getting at most two Tails = {TTH, THT, HTT, THH, HTH, HHT, HHH}
A bag contains 4 black, 5 yellow and 6 green balls. Three balls are drawn at random from the bag. What is the probability that all of them are yellow?
Total number of balls = 4 + 5 + 6 = 15
Let S be the sample space.
Let E = Event of drawing 3 balls, all of them are yellow.
[∵ ^{n}C_{r} = ^{n}C_{(}_{nr)}. So ^{5}C_{3} = ^{5}C_{2}. Applying this for the ease of calculation]
A bag contains 2 yellow, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
Total number of balls = 2 + 3 + 2 = 7
► Let S be the sample space.
► Let E = Event of drawing 2 balls, none of them is blue.
There are 15 boys and 10 girls in a class. If three students are selected at random, what is the probability that 1 girl and 2 boys are selected?
Let S be the sample space.
Let E = Event of selecting 1 girl and 2 boys
15 boys and 10 girls are there in a class. We need to select 2 boys from 15 boys and 1 girl from 10 girls
Number of ways in which this can be done:
^{15}C_{2} × ^{10}C_{1}
Hence n(E) = ^{15}C_{2} × ^{10}C_{1}
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