Sum of Probabilities of Favorable and Unfavorable Event

Q. If the probability of winning a race of an athlete is $\frac{1}{6}$ less than twice the probability of losing, find the probability of losing the race.

1. $\frac{7}{18}$
2. $\frac{1}{3}$
3. $\frac{3}{4}$
4. $\frac{5}{6}$

Q. A coin is tossed five times, find the probability of getting no head.

1. $\frac{1}{30}$
2. $\frac{5}{32}$
3. $0.4$
4. $\frac{1}{32}$

Q.

Cards were drawn from a regular deck of 52 for a 100 times, replacing it each time after drawing. The data about the number is as follows.

$$\begin{array}{cc}\text{Number}& \text{Frequency}\\ A& 10\\ 2& 8\\ 3& 5\\ 4& 6\\ 5& 8\\ 6& 5\\ 7& 10\\ 8& 11\\ 9& 8\\ 10& 7\\ J& 6\\ Q& 7\\ K& 9\end{array}$$

(i) Find the probability of drawing a face card ;

(ii) Find the probability of drawing a number card with a prime number on it . [2MARKS]
.

Q. If a coin is tossed twice, find the probability of getting at least one head.

1. $\frac{1}{2}$
2. $\frac{1}{4}$
3. $\frac{3}{4}$
4. $\frac{2}{3}$

Q. The proability of having at least one tail in $4$ throws with a coin is

1. $15/16$
2. $1/16$
3. $1/4$
4. $1$