Question

The probability that two independent events both occur is the sum of the probabilities of each independent event. 4. When choosing a card randomly from a deck of cards, choosing a 5 or a spade are not

Answer 1

(i) False

(ii) Selecting a 5 or a spade are not independent.

Explanation:

(i)

Independent events are those events that occur at the same time, i.e. the occurrence of one event does not effects the occurrence of the other.

If A and B are independent events then:
`P(A\cap B)=P(A)* P(B)`

Whereas as if two events are mutually exclusive, then the probability of them both taking place at the same time is 0.

Then for events A and B:
`P(A\cap B)=0`

Thus, the statement is False.

(ii)

In a standard deck of 52 cards there are:

Spades = 13

Diamond = 13

Heart = 13

Clubs = 13

And each of these 13 cards are:

K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3, 2, A

If a card labelled as 5 is selected then it could also be a Spade.

And if a spade is selected then the card could be labelled as 5.

So, selecting a 5 or a spade are not independent.