Quiz-1

Probability of getting head in one trail = 1/2
∴ Reqd Probability of getting heads in both the trails = 1/2 x 1/2 = 1/4

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

Required probability = P(A) x P(B)
= (7/8) x (9/10)
= 63/80

Total number of cards n(S) = 52
Number of red cards n(E) = 26
∴ P(E) = n(E)/n(S) = 26/52 = 1/2

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

n(S) = Number of ways of drawing 2 balls out of 13 = ¹³C₂ = (13 × 12) / 2= 78
n(E) = No. of ways of drawing 2 balls out of 5 = ⁵C₂ = 10

∴ P(E) = n(E)/n(S) = 10/78 = 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) = n(E)/n(S) = 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 = 1/5 x 2/3 + 4/5 x 1/3
= 2/15 + 4/15 = 6/15 = 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 =4⁴/10⁴
= 2⁴/5⁴ = 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 = 16/52 = 4/13