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प्रश्न
A card is selected from a pack of 52 cards.
- How many points are there in the sample space?
- Calculate the probability that the card is an ace of spades.
- Calculate the probability that the card is
- an ace
- black card.
उत्तर
a. There are 52 cards in a deck of cards. When a card is drawn, its sample space has 52 points.
b. There is an ace of spades in a deck of cards. If A denotes the event of drawing a card, then
n(A) = 1, n(S) = 52
P(A) = P(ace of spades) = `1/52`
c. (i) If B denotes drawing an ace, then
n(B) = 4 … [∵ There are 4 aces in a deck of cards.]
n(S) = 52
∴ P(B) = `1/13`
(ii) C denotes the event of drawing a black spades card.
n(C) = 26 ... [∵ There are 26 black cards in a pack of cards.]
n(S) = 52
∴ P(C) = `26/52`
= `1/2`
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संबंधित प्रश्न
Which of the following can not be valid assignment of probabilities for outcomes of sample space S = {ω1, ω2,ω3,ω4,ω5,ω6,ω7}
| Assignment | ω1 | ω2 | ω3 | ω4 | ω5 | ω6 | ω7 |
| (a) | 0.1 | 0.01 | 0.05 | 0.03 | 0.01 | 0.2 | 0.6 |
| (b) | `1/7` | `1/7` | `1/7` | `1/7` | `1/7` | `1/7` | `1/7` |
| (c) | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 |
| (d) | –0.1 | 0.2 | 0.3 | 0.4 | -0.2 | 0.1 | 0.3 |
| (e) | `1/14` | `2/14` | `3/14` | `4/14` | `5/14` | `6/14` | `15/14` |
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