2. If a card is drawn from a regular deck of cards, what is the probability that

Question

2. If a card is drawn from a regular deck of cards, what is the probability that the card is a jack or/black card? (8 points each) 3. The Bargain Auto Mall has these cars in stock. Foreign20 50 Domestic 65 If a car is selected at random, find the probability that the car is a. Foreign or Compact SUV Compact Mid-sized 20 100 45 b. Mid-sized and Foreign 4, A recent survey stated that 70% of college student have a smart phone. If four students are selected at random, what is the probability that none have smart phone? (8 points)

Explanation / Answer

2) A regular deck has 26 black cards and 4 jacks, of which 2 are black.

P(Event) = Favourable outcomes/Total outcomes

Total outcomes- Drawing 1 card out of 52 = 52 outcomes

Favourable outcomes = 26 + 4 - 2 = 28(As the 2 black Jacks are counted twice)

Therefore the required probability = 28/52 = 7/13

3) The complete table is as follows

There are a Total of 300 cars, which is our Total outcomes

(a) Foreign or Compact: Favourable outcomes = 90 + 150 - 50 = 190 (As the foreign and compact gets counted twice).

Therefore the required probability = 190/300 = 19/30

(b) Mid Sized and Foreign: Favourable outcomes = 20

Therefore the required probability = 20/300 = 1/15

4) This question deals with Binomial probability.

Binomial Probability = nCx * (p)x * (q)n-x, where n = number of trials and x is the number of successes.

Here n = 4, x = 0, n – x = 4 - 0 = 4, p = 0.7, q = 1 – p = 1 - 0.7 = 0.3

P(x = 0) = 4C0 * (0.7)0 * (0.3)4 = 0.0081

SUV Compact Mid-Sized Total Foreign 20 50 20 90 Domestic 65 100 45 210 Total 85 150 65 300

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