Probability of multiple events happening at a time (a turn)

Q1. If two people are selected at random, find the probability that both wereborn on Wednesday.
Each person has approximately one chance in seven of being born on Wednesday; hence, the probability that two people are born on Wednesday is

Q2. The probability that a person A will be alive 15 year hence is 5/7 and the probability that another person B will be alive 15 years hence is 7/9. Find the probability that both will be alive 15 year hence.
Let event
A = when A will be alive, thus P(A)=5/7 (given)
B = when B will be alive, thus P(B)=7/9 (given)
Required probability is

Q3. A coin is tossed and a card is selected at random from a deck of 52 cards. Find the probability of getting a head and a diamond on the card.
The probability of getting a head is½, and the probability of getting adiamond is 13/52=¼; hence, the P(head and diamond).
P(H)∙P(diamond)= ½∙¼=⅛

Independent Events

Suppose box X contains 2 blue and 2 green balls, and box Y contains 1 white and 3 red balls. A ball is randomly selected from 1 each of the boxes. Determine the probability of getting “a blue ball from X and a red ball from Y”.

By illustrating the sample space on the two-dimensional grid shown, We can see that 6 of the 16 possibilities are blue from X and red from Y. Each of the outcomes is equally likely, so

In this section we look for a quicker method for finding the box); probability in such a situation.
independent events

Let’s read more explanation about Independent Events in the post Probability: Independent Events.


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