A bag contains 15 one rupee coins, 25 two rupee coins and 10 five rupee coins. If a coin is selected at random from the bag, then the probability of not selecting a one rupee coin is (A) 0.30 (B) 0.70 (C) 0.25 (D) 0.20
ANSWER
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Hint: We will start our solution by finding out the total number of coins. Then we will use a probability formula to find out the probability of not selecting a one rupee coin and solve accordingly.
Complete step-by-step solution - Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e. how likely they are to happen, using it. Probability can range in between 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event. Probability for class 10 is an important topic for the students which explains all the basic concepts of this topic. The probability of all the events in a sample space sums up to 1. The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favourable outcomes and the total number of outcomes. Probability of an event to happen, \[\begin{gathered} \Rightarrow {\text{P(E) = }}\dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Total number of outcomes}}}} \\ \Rightarrow {\text{P(E) = }}\dfrac{{{\text{Total number of outcomes}} - {\text{Number of unfavourable outcomes}}}}{{{\text{Total number of outcomes}}}} \\ \end{gathered} \] Given that, Total number of one rupee coins = 15, Total number of two rupee coins = 25, Total number of five rupee coins = 10. Therefore, Total number of coins = 15 + 25 + 10, Total number of coins = 50. We know that we have to select a coin randomly from the bag. Given that the coin selected is not a one rupee coin. It means either we can select a two rupees coin or a five rupees coin. Therefore, probability of not selecting a coin is equal to the sum of the probability of selecting a two rupees coin or a five rupees coin: $\begin{gathered} \Rightarrow P(E) = \dfrac{{{\text{Total number of coins - Total number of one rupee coins }}}}{{{\text{Total number of coins}}}} \\ \Rightarrow P(E) = \dfrac{{{\text{Total number of two rupees and five rupees coin }}}}{{{\text{Total number of coins}}}} \\ \end{gathered} $ $\begin{gathered} \Rightarrow {\text{P(E)}}\,{\text{ = }}\dfrac{{25 + 10}}{{50}} \\ \Rightarrow {\text{P(E)}}\,{\text{ = }}\dfrac{{35}}{{50}} \\ \Rightarrow {\text{P(E)}}\,{\text{ = }}\dfrac{7}{{10}} \\ \Rightarrow {\text{P(E)}}\,{\text{ = }}\,{\text{0}}{\text{.70}} \\ \end{gathered} $ Therefore, the probability of not selecting a one rupee coin is 0.70. Hence, the correct answer is option (B) 0.70.
Note: For solving this type of question, knowing the formula of probability is the key here. The probability is positive and less than or equal to 1. The probability of the sure event is 1. The sum of probabilities of an event and its complement is 1.