Given:
A standard deck has 52 cards:
Diamonds = 13 cards
Spades = 13 cards
Four cards are drawn at random.
Step 1: Find the total number of ways to draw 4 cards
Total ways =
52C4
Step 2: Find the number of favourable outcomes
To obtain exactly 3 diamonds and 1 spade:
Ways to choose 3 diamonds from 13 =
13C3
Ways to choose 1 spade from 13 =
13C1
Total favourable outcomes =
13C3 × 13C1
Step 3: Calculate the probability
Probability =
( Number of favourable outcomes ) / ( Total number of outcomes )
= ( 13C3 × 13C1 ) / 52C4
Step 4: Simplify (optional)
13C3 = 286
13C1 = 13
52C4 = 270725
Probability =
(286 × 13) / 270725
= 3718 / 270725
Final Answer:
The probability of obtaining 3 diamonds and 1 spade is
( 13C3 × 13C1 ) / 52C4
Two dice are thrown. The events A, B and C are as follows:
A: getting an even number on the first die.
B: getting an odd number on the first die.
C: getting the sum of the numbers on the dice ≤5.
State true or false: (give reason for your answer)
(i) A and B are mutually exclusive
(ii)A and B are mutually exclusive and exhaustive
(iii) A=B′
(iv)A and C are mutually exclusive
(v)A and B′ are mutually exclusive.
(vi) A′,B′,C are mutually exclusive and exhaustive.
From the employees of a company, \(5\) persons are selected to represent them in the managing committee of the company. Particulars of five persons are as follows: A person is selected at random from this group to act as a spokesperson. What is the probability that the spokesperson will be either male or over \(35\) years?