Question

8. In a hospital, 30% of the staff are female, and 50% of the staff walk to hospital. If 20% of the staff is female and walk to hospital, what is the probability that a randomly chosen staff is female or walks to hospital?

9. A card is drawn randomly from a standard deck of cards. What is the probability that the card drawn is a 2 or a Spade? Details and Assumptions: A standard deck of cards consists of 52 cards, formed by 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen and King) of 4 suits (clubs, diamonds, hearts and spades).

Answer 1

Solution:

Question 8)

Given:

In a hospital, 30% of the staff are female, thus P(Female) = 0.30

50% of the staff walk to hospital, thus P( Staff walk to hospital) = 0.50

20% of the staff is female and walk to hospital, thus P( Female and walk to hospital) =0.20

We have to find:

P( a randomly chosen staff is female or walks to hospital ) =.............?

P( Female or walks to hospital ) =.............?

Using addition rule of probability, we get:

P( Female or walks to hospital ) = P(Female) + P( Staff walk to hospital) - P( Female and walk to hospital)

P( Female or walks to hospital ) = 0.30 + 0.50 - 0.20

P( Female or walks to hospital ) = 0.60

.

Question 9)

Given: A card is drawn randomly from a standard deck of cards.

We have to find:

P(  the card drawn is a 2 or a Spade ) =.................?

P( 2 or Spade) = ..........?

Thus using addition rule of probability, we get:

P( 2 or Spade) = P(2) + P(Spade) - P( 2 and Spade)

In standard deck of 52 playing cards, we have 4 cards of number "2" and 13 cards of "Spade".

Also we have a card of number "2" which is a spade.

Thus

P(getting number "2") =P(2) = 4/52

P( getting a spade ) = P( Spade) = 13/52

and

P( Getting both number "2" and Spade) =P( 2 and Spade) = 1/52

Thus

P( 2 or Spade) = P(2) + P(Spade) - P( 2 and Spade)

P( 2 or Spade) = 4/52 + 13/52 - 1/52

P( 2 or Spade) = ( 4+13-1) / 52

P( 2 or Spade) = 16/52

P( 2 or Spade) = 4 / 13