In a town 45% people speak English, 30% speak Hindi and 20% speak both English and Hindi. One person is selected at random. Find the probability that he speaks English, if it is known that he speaks Hindi.
There are 8 brown balls, 4 orange balls and 5 black balls in a bag. Five balls are chosen at random. What is the probability of their being 2 brown balls, 1 orange ball and 2 black balls ?
When 4 fair coins are tossed simultaneously, the total number of outcomes is 24 = 16
At least 3 heads implies that one can get either 3 heads or 4 heads.
One can get 3 heads in 4C3 = 4 ways and can get 4 heads in 4C4 = 1 ways.
∴ Total number of favorable outcomes = 4 + 1 = 5
====>>> The required probability = 1/4.
or
The answer is 5/16 because in total there are 16 possibilities when tossing a coin 4 times. I.e. 2⋅2⋅2⋅2=242⋅2⋅2⋅2=24.
And the possibilities of getting atleast three head is 5 that is we can get HHHT, HHTH, HTHH, THHH, and HHHH
Thus, the answer is 5/16.
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A basket contains 10 apples and 20 oranges out of which 3 apples and 5 oranges are defective. If we choose two fruits at random, what is the probability that either both are oranges or both are non defective?
A pot contains 5 white and 3 red balls while another pot contains 4 white and 6 red balls. One pot is chosen at random and a ball is drawn from it. If the ball is white, what is the probability that it is from the first pot?
The probability of choosing one pot = 1/2
The probability of choosing white ball in first pot = 1/2 × [ 5C1 / 8C1] = 5/16
The probability of choosing white ball
= 1/2 × [5C1 / 8C1] + 1/2 × [4C1 / 10C1]
= 1/2 × [5/8] + 1/2 × [4/10]
= 5/16 + 1/5 = 41/80 ∴ The probability that it is from the first pot = (5/16) / (41/80)
= 5/16 × 80/41 = 25/41
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In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?
A man and his wife appear in an interview for two vacancies in the same post. The probability of husband’s selection is (1/7) and the probability of wife’s selection is (1/5). What is the probability that only one of them is selected ?
