1. Consider drawing a single card from a standard deck. For each part la and 1b,

Question

1. Consider drawing a single card from a standard deck. For each part la and 1b, (i) Determine whether the events are disjoint. (ii) Compute the probability (a) Drawing a 2 or a face card when drawing a card from a standard deck. (b) Drawing a Jack or a face card when drawing a card from a standard deck 2. Consider a situation where you are picking a number from [0, 4]. The software you are using randomly selects a number following the percentage breakdown below 0,1 12)12,3) 3,4 20% | 10% | 30% 40% (a) What is the random variable? Is it continuous or finite? (b) Write the probability distribution c) Find P(X 3 2.7)

Explanation / Answer

Solution(1):

We are given that : a single card is drawn from the standard deck.

we have to determine if events are disjoint or not and then compute probability.

a) Drawing a 2 or a face card when a drawing a card from standard deck.

Let A = Event of getting a card of 2

B = Event of getting a Face card

Since getting a 2 and getting a Face is not possible or they are mutually exclusive events,

P( A and B) = P( getting a 2 and a Face card ) = 0

Thus Events A and B are disjoint.

Thus

P( A or B) = P( A) + P( B) - P( A and B)

where

P(A) = P( Drawing a card of 2) = 4/52

Since there are 4 cards of number 2.

P(B) = P( Drawign a Face card ) = 12 / 52

Since there are 12 face cards in standard deck ( 4 Jack + 4 Queen + 4 King = 12 Face cards)

and

P( A and B) = 0

Thus

P( A or B) = 4/52 + 12/52   - 0

P( A or B) = 16 / 52

P( A or B) = 4 / 13

P( A or B) =0.3077

Thus P( drawing a 2 or a Face card) = 0.3077

Part b) Drawing a Jack or a Face card when drawing a card from a standard deck.

Let A = Drawing a Jack card

B = Drawing a Face card.

There are 4 cards of Jack which are also Face cards.

Thus P( A and B) = 4/52

Thus events Drawing a Jack and Drawing a Face card are not disjoint.

P( A or B) = P( A) + P( B) - P( A and B)

where

P(A) = P( Drawing a Jack ) = 4/52

Since there are 4 cards of Jack.

P(B) = P( getting a Face card ) = 12 / 52

Since there are 12 face cards in standard deck ( 4 Jack + 4 Queen + 4 King = 12 Face cards)

and

P( A and B) = 4/52

Thus

P( A or B) = 4 / 52 + 12 / 52 -   4 / 52

P( A or B) = 12 / 52

P( A or B) = 3 / 13

P( A or B) = 0.2308

Thus

P( Drawing a Jack or a Face card) = 0.2308

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