A coin is tossed $7$ times. Each time a man calls head. Find the probability that he wins the toss on more occasions.
- $\frac{2}{3}$
- $\frac{1}{2}$
- $\frac{3}{4}$
- $\frac{1}{3}$
The Correct Option is B
Solution and Explanation
$\therefore $ Reqd. probability =
$^{7}C_{4} \left(\frac{1}{2}\right)^{4} .\left(\frac{1}{2}\right)^{3} + ^{7}C_{5} \left(\frac{1}{2}\right)^{5} . \left(\frac{1}{2}\right)^{2} + ^{7}C_{6} \left(\frac{1}{2}\right)^{6} . \frac{1}{2} + ^{7}C_{7} \left(\frac{1}{2}\right)^{7} $
$ = \left(^{7}C_{4} + ^{7}C_{5} + ^{7}C_{6} + ^{7}C_{7}\right) . \frac{1}{2^{7}} = \frac{64}{2^{7}} = \frac{1}{2} $
Top Questions on Event
- For two events A and B, if \(P(A) = P(A/B) = \frac{1}{4}\) and \(P(B/A) = \frac{1}{2}\), then which of the following is not true?
- If \( \frac{1 + 3p}{4}, \frac{1 - p}{3}, \frac{1 - 3p}{2} \) are the probabilities of three mutually exclusive and exhaustive events, then the value of \( p \) is:
- A coin is tossed three times. If X denotes the absolute difference between the number of heads and the number of tails then P(X = 1) =
- A boy is throwing stones at a target. The probability of hitting the target at any trial is $\frac{1}{2}$ .The probability of hitting the target $5^{th}$ time at the $10^{th}$ throw is :
- Two dice are thrown together $4$ times. The probability that both dice will show same numbers twice is -
Questions Asked in BITSAT exam
In the given cycle ABCDA, the heat required for an ideal monoatomic gas will be:
- BITSAT - 2024
- specific heat capacity
A conducting wire is stretched by applying a deforming force, so that its diameter decreases to 40% of the original value. The percentage change in its resistance will be:
- BITSAT - 2024
- thermal properties of matter
- Identify, from the following, the diamagnetic, tetrahedral complex:
- BITSAT - 2024
- The solid state
- Inside a solenoid of radius \( 0.5 \) m, the magnetic field is changing at a rate of \( 50 \times 10^{-6} \) T/s. The acceleration of an electron placed at a distance of \( 0.3 \) m from the axis of the solenoid will be:
- BITSAT - 2024
- thermal properties of matter
- Young's double slit experiment is performed in a medium of refractive index \( 1.33 \). The maximum intensity is \( I_0 \). The intensity at a point on the screen where the path difference between the light coming out from slits is \( \lambda/4 \), is:
- BITSAT - 2024
- Dual nature of radiation and matter
Concepts Used:
Event
A probability event can be defined as a set of outcomes of an experiment. In other words, an event in probability is the subset of the respective sample space. The likelihood of occurrence of an event is known as probability. The probability of occurrence of any event lies between 0 and 1.
Thus, an event is a subset of the sample space, i.e., E is a subset of S.
There could be a lot of events associated with a given sample space. For any event to occur, the outcome of the experiment must be an element of the set of event E.
Probability of Occurrence of an Event
P(E) = Number of Favourable Outcomes/ Total Number of Outcomes
Types of Events in Probability:
Some of the important probability events are:
- Impossible and Sure Events
- Simple Events
- Compound Events
- Independent and Dependent Events
- Mutually Exclusive Events
- Exhaustive Events
- Complementary Events
- Events Associated with “OR”
- Events Associated with “AND”
- Event E1 but not E2