# Combinatorics in Calculating Probabilities for Multiple Events

## Trending Questions

**Q.**

A mail-order company business has six telephone lines.

Let X denote the number of lines in use at a specified time.

Suppose the p. m .f of $X$ is as given in the accompanying table.

$x$ | 0 | 1 | 2 | 3 | 4 | 5 | 6 |

$\mathrm{P}\left(x\right)$ | 0.10 | 0.15 | 0.20 | 0.25 | 0.20 | 0.05 | 0.05 |

Calculate the probability of each of the following events.

(a) {at most three lines are in use}

(b) {fewer than three lines are in use}

(c) {at least three lines are in use}

(d) {between two and five lines, inclusive, are in use}

(e) {between two and four lines, inclusive, are not in use}

(f) {at least four lines are not in use}

**Q.**3 balls are selected at random from a bag containing 4 red and 5 blue balls. Find the probability that atleast 1 red ball is selected.

- 4C1× 5C2 9C3+ 4C2× 5C1 9C3

+ 4C3 9C3

- 4C1× 5C2 9C3+ 4C2× 5C1 9C3

- 4C1× 5C2 9C3+ 4C3 9C3

- 4C2× 5C1 9C3+ 4C3 9C3

**Q.**A card is drawn at random from a deck of 52 cards. Find the probability of drawing a heart or spade.

- 14

- 12

- 113

- 152

**Q.**In an experiment of tossing a coin, if head is obtained then the coin is tossed again and if tail is obtained then a die is rolled. What is the probability of obtaining a tail on the coin and number 3 on the die?

- 18

- 16

- 12

- 112

**Q.**A store has six different fitness magazines and three different news magazines. If a customer buys four magazines at random, what is the probability that the customer will buy three fitness magazines and one news mgazine?

- 27
- 37
- 47
- 57

**Q.**A child randomly selects 4 toys from a box containing 2 bunnies, 5 dogs and 3 bears. Find the probability that 2 dogs and 2 bears are chosen.

- 5C2× 3C2 10C4

- 5C2 10C4

- 3C2 10C4

- 5C2+ 3C2 10C4

**Q.**

When a certain coin is flipped, the probability of obtaining a tails is $0.60$. Which of the following is the probability that tails would be obtained exactly $10$ times when the coin is flipped $20$ times?

$0.0473$

$0.1171$

$0.1762$

$0.2447$

$0.50$

**Q.**Alexa has an important meeting in the morning. She sets three battery-powered alarm clocks just to be safe. If the first alarm clock has a 1 4C1 probability of malfunctioning, second alarm clock has a 1 3C1 probability of malfunctioning and the third alarm clock has a 1 5C1 probability of malfunctioning, what is the probability that all the three alarm clocks fail at the same time?

- 112

- 115

- 120

- 160

**Q.**Ian gave each of his 2 buddies a candy at his birthday celebration, with the treats being 2 Hazel Nut bars, 2 Coconut Milk bars, and 1 Dates bars. What is the probability that both of Ian's friends got the same type of candy?

- 15
- 25
- 110
- 45

**Q.**A lucky draw machine is filled with 10 colored balls as 5 red, 3 green, and 2 blue. Machine selects 2 balls one by one withouth replacement. What is the probability that no two balls are of the same color?

- 3145
- 1445
- 1345
- 3245