The Probability 1 category gathers fundamental probability problems, covering basic concepts such as events, outcomes, and simple calculations. It helps learners practice and reinforce their understanding of probability fundamentals.
Let's break it down: we verify 35 by full calculation: use standard identity, substitute, simplify step by step to reach 35.
Ref: NCERT Mathematics Class XII — Probability
The logic is straightforward: we verify 5/7 by full calculation: use standard identity, substitute, simplify step by step to reach 5/7.
Ref: NCERT Mathematics Class XII — Probability
The trick is we verify 12 by full calculation: use standard identity, substitute, simplify step by step to reach 12.
Ref: NCERT Mathematics Class XII — Probability
Simply put, complete solution: write formula, plug data, do arithmetic. Final value matches 1/2;and;7/8. Simple and accurate.
Ref: NCERT Mathematics Class XII — Probability
In easy words, using formula we get P(A) + P(B). Calculation gives this directly, check steps: apply rule, substitute values, simplify to get P(A) + P(B).
Ref: NCERT Mathematics Class XII — Probability
In easy words, np=4, npq=3 gives q=0.75,p=0.25,n=16. Mode=floor((n+1)p)=floor(4.25)=4. Complete.
Ref: NCERT Mathematics Class XII — Probability
We can see that complete solution: write formula, plug data, do arithmetic. Final value matches 300. Simple and accurate.
Ref: NCERT Mathematics Class XII — Probability
Applying the basic concept, we verify 3 by full calculation: use standard identity, substitute, simplify step by step to reach 3.
Ref: NCERT Mathematics Class XII — Probability
We can see that binomial n=6, p=0.5. P=6C2(1/2)^6=15/64. Calculation: 6C2=15, (1/2)^6=1/64.
Ref: NCERT Mathematics Class XII — Probability
Recall the rule success getting 4: p=1/6, n=72, q=5/6. Variance=npq=72×1/6×5/6=10. Complete formula.
Ref: NCERT Mathematics Class XII — Probability
In easy words, 3·5C2 p²q³=5C3 p³q², so 30q=10p, 3(1-p)=p, 3-3p=p, p=3/4. Complete solving.
Ref: NCERT Mathematics Class XII — Probability
Think of it like this: p=0.5, n=5. P(at most 1 negative)=P0+P1= C5,0(0.5)^5+C5,1(0.5)^5=1/32+5/32=6/32=3/16. Full.
Ref: NCERT Mathematics Class XII — Probability
