Deloitte Probability Questions and Answers Quiz-1

Probability of getting head in one trail = \frac{1}{2}
∴ Reqd Probability of getting heads in both the trails = \frac{1}{2} \times \frac{1}{2}= \frac{1}{4}

Total ways = 52
There is one queen of club and one king of heart favourable ways = 1 + 1 = 2.
∴ Required probability =\frac{2}{52} = \frac{1}{26}

Required probability = P(A) x P(B)
= \frac{7}/{8} \times {9}{10}
= \frac{63}{80}

Total number of cards n(S) = 52
Number of red cards n(E) = 26
∴ P(E) = \frac{n(E)}{n(S)} = \frac{26}{52} =\frac{1}{2}

n(S) = 36
n(E) = {(5,6), (6,5)} = 2
∴ p(E) = \frac{n(E)}{n(S)} = \frac{2}{36} = \frac{1}{18}

n(S) = Number of ways of drawing 2 balls out of 13 = 13C2 = 13 \times \frac{12}{2}= 78
n(E) = No. of ways of drawing 2 balls out of 5 = 5C2 = 5 \times \frac{4}{2}= 10

∴ P(E) = \frac{n(E)}{n(S)} = \frac{10}{78} = \frac{5}{39}

n(S) = (2)3 = 8
E = Event of getting 0, or 1 or 2 heads
= {TTT, TTH, THT, HTT, HHT, HTH, THH}
⇒ n(E) = 7
∴ P(E) = \frac{n(E)}{n(S)} =\frac{7}{8}

One of them can be selected in the following ways.
Brother is selected and sister is not selected.
or
Brother is not selected and sister is selected.

∴ Required probability =\frac{1}{5} \times \frac {2}{3} + \frac{4}{5} \times \frac{1}{3}
= \frac{2}{15} +\frac{4}{15} = \frac{6}{15} =\frac{2}{5}

If the product of the four numbers ends in one of the digits 1, 3, 7 or 9, each number
should have the last digit as one of these 4 digits.
∴ The number of favourable cases = 4⁴
Total number of all possible cases = 10⁴
Hence, the required probability = \frac{4^{4}}{10^{4}} = \frac{2^{4}}{5^{4}} = \frac{16}{625}

Total ways = 52
There are 13 cards of diamond, 4 cards of king, but one card is king of diamond which
is counted both in diamond and king cards
⇒ Favourable ways = 13 + 4 - 1 = 16
∴ Required probability = \frac{16}{52} =\frac {4}{13}