From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is_________?

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From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is_________?

A. 1/26
B. 3/52
C. 15/26
D. 11/26
Explanation:
Let E1 be the event of drawing a red card.
Let E2 be the event of drawing a king .
P(E1 ∩ E2) = P(E1) . P(E2)
(As E1 and E2 are independent)
= 1/2 * 1/13 = 1/26

Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?

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Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?

A. 1/6
B. 5/8
C. 3/8
D. 5/6
Explanation:
P(at least one graduate) = 1 – P(no graduates) =
1 – ⁶C₃/¹⁰C₃ = 1 – (6 * 5 * 4)/(10 * 9 * 8) = 5/6

The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?

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The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?

A. 18/35
B. 12/35
C. 17/35
D. 19/35
Explanation:
If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 4/7 + 2/5 * 3/7
= 12/35 + 6/35 = 18/35

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?

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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. 5/21
B. 5/14
C. 9/14
D. 16/21
Explanation:
Number of ways of (selecting at least two couples among five people selected) = (⁵C₂ * ⁶C₁)
As remaining person can be any one among three couples left.
Required probability = (⁵C₂ * ⁶C₁)/¹⁰C₅
= (10 * 6)/252 = 5/21

The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on at least one ticket is__________?

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The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on at least one ticket is__________?

A. 0.4869
B. 0.5904
C. 0.6234
D. 0.5834
Explanation:
P(winning prize atleast on one ticket)
= 1 – P(“Losing on all tickets”)
= 1 – (0.8)4 = (1 + (0.8)2)(1 – (0.8)2)
= (1.64)(0.36) = 0.5904

10 books are placed at random in a shelf. The probability that a pair of books will always be together is_________?

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10 books are placed at random in a shelf. The probability that a pair of books will always be together is_________?

A. 1/10
B. 9/10
C. 1/5
D. 3/10
Explanation:
10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability = 1/5