**Probability Shortcut Tricks Questions and Answers Math Tricks:**

If you are preparing for **SBI, IBPS PO, IBPS SO, AAO, RPSC, UPSC** then probability is the very important topic of math. Now we are discussing on the theory of probability with problems and solutions. Probability can be said a chance to something happening.

**Probability Theory:** Probability can be said a chance to something happening. The probability of an event happening can’t be a negative number or greater than 1. The chance of probability ranges from 0 to 1. We take a example of coin, if we flip a coin into air then two things can happen after reaching the ground of coin. It can be happen two events either Head or Tail. So total events will occur are 2 and it can either Head or Tail. So the Probability of Head or Tail is ½.

**Further we are providing formulas or short cut tricks to solve Probability Questions:**

**Probability of Event Happening= **Regards Events/Total Events

**Probability of Event Happening= **P[E]

**Probability of Not Happening a Event=** P(Ē)

And **P(E) + P(Ē) = 1**

**Note-** If ‘and’ occur than we count or multiply all the events. If ‘or’ occur than we add two or more events.

Probability Questions with Solutions According to Previous Years Papers of SBI, IBPS and Other;

**Question 1:** Calculate the probability of getting a sum of 8 on rolling a dice twice??

**Solution:** we look that the concerned events can be sum of 8 So the total Concerned Events: (6,2), (4,4), (5,3), (2,6) and (3,5)

Total Concerned Events= 5

Total Events can occur for Dice= 36

Probability= 5/36

**Question 2:** Calculate the Probability of getting a Tail in a toss??

**Solution:** Concerned Event= 1 (Tail)

Total Events= 2

So Probability P(E)= ½

**Question 3:** Calculate the probability of getting a King of Spade or Queen of Heart in one Draw of cards??

**Solution:** The ‘King of Spade or Queen of Heart’ means that either card can be Spade King or Heart Queen. So its clear that there is only one King of Spade and only one Queen of Heart.

So Concerned Events= 2

Total Events= 52

Probability P(E)=2/52=1/26

**Question 4:** Calculate the probability of drawing two balls of same colors if a box contains 10 black or 10 white balls???

**Solution:** Total Events from 20 Balls if 2 balls are drawn= ^{20}C_{2}

We can say that balls drawn can either be both black or both white color, So here ‘Or’ occur than we add two events

Concerned Event= ^{10}C_{2 }+ ^{10}C_{2}

So Probability P(E)= (^{10}C_{2 }+ ^{10}C_{2}/^{20}C_{2}) = 10*9+10*9/20*19= 9/19

**Question 5:** Suppose that X and Y give exam. The chance of X’s selection is 1/7 and of Y’s selection is 1/5. Calculate the probability of only one of them is selected??

**Solution:** Probability of X’s selecting: 1/7

Probability of X’s not selecting= 1-1/7= 6/7

Probability of Y’s selecting= 1/5

Probability of Y’s not selecting= 1-1/5 =4/5

Probability of one of them selected= P(X’s selection)* P(Y’s not selection)+ P(Y’s selecting)*P(X not selecting) = (1/7*4/5)+(1/5*6/7)= 10/35= 2/7